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On a decomposition of Banach spaces

Jakub Duda (2007)

Colloquium Mathematicae

By using D. Preiss' approach to a construction from a paper by J. Matoušek and E. Matoušková, and some results of E. Matoušková, we prove that we can decompose a separable Banach space with modulus of convexity of power type p as a union of a ball small set (in a rather strong symmetric sense) and a set which is Aronszajn null. This improves an earlier unpublished result of E. Matoušková. As a corollary, in each separable Banach space with modulus of convexity of power type p, there exists a closed...

On a decomposition of non-negative Radon measures

Bérenger Akon Kpata (2019)

Archivum Mathematicum

We establish a decomposition of non-negative Radon measures on ℝ d which extends that obtained by Strichartz [6] in the setting of α -dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.

On a function that realizes the maximal spectral type

Krzysztof Frączek (1997)

Studia Mathematica

We show that for a unitary operator U on L 2 ( X , μ ) , where X is a compact manifold of class C r , r ∈ ℕ ∪ ∞ , ω , and μ is a finite Borel measure on X, there exists a C r function that realizes the maximal spectral type of U.

On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

Let Ti (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ Lp(μ) the averagesAnf(x) = (n + 1)-d Σ0≤ni≤n f(T1n1T2n2 ... Tdnd x)converge a.e. on X if and only if there exists a finite invariant measure ν (under the transformations Ti) absolutely continuous with respect to μ and a sequence {XN} of invariant sets with XN ↑ X such that νB > 0 for all nonnull invariant sets B and...

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